The downstream decay of trapped lee waves

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Abstract

The mechanisms through which trapped lee waves decay, and where this decay occurs, are of utmost importance in order to understand the impact that these waves have on the larger-scale climate system. Previous studies have shown trapped waves as contributing a significant fraction of the total orographic drag, but they remain poorly understood. In this dissertation, two decay mechanisms are analyzed and compared --- stratospheric leakage, and boundary layer absorption. Decay of lee waves through upward leakage of wave energy towards the stable stratosphere is studied primarily using a linear Boussinesq model, forced by either a three-layer atmosphere or a more realistic four-layer atmosphere containing vertical wind shear and an elevated inversion. Weak downstream decay occurs due to the stratosphere in the highly-idealized three-layer atmosphere, albeit at too slow of a rate for the typical decay seen in nature. In the more realistic profile, rapid downstream decay occurs through stratospheric leakage --- leading to a removal of the wavetrain within 1.5 wavelengths in the most extreme case of a 200 m deep elevated inversion. As the depth the elevated inversion is reduced, the potential rate of downstream decay is increased. For all profiles, the rate of leakage due to the stratosphere is shown to be maximized for values of stratospheric stability (N<sub>s</sub>) slightly larger than for the threshold for decay, with a decreasing trend in the rate of decay as the stratospheric stability is further increased. The impact of the stratosphere and boundary layer on trapped wave decay are both simulated using a full nonlinear numerical model. Decay through boundary layer absorption is seen to vary slightly with the atmospheric profile --- relating to the location and the structure of the resonant wave duct compared to the boundary layer. Rates of downstream decay due to the stratosphere agree well between the linear and nonlinear models. Given the highly-idealized atmospheric profile, boundary layer decay is dominant with minimal decay occurring through stratospheric leakage at any N<sub>s</sub>. With the realistic profile shown by the linear model to be suitable for strong stratospheric leakage, downstream decay is stronger due to the stratosphere than for the roughest lower boundary simulated (z<sub>0</sub> = 0.5 m, where z<sub>0</sub> is the roughness length). A move towards understanding the decay of trapped waves in three dimensions is also discussed through use of high-resolution simulations of lee waves downwind of the Aleutian islands using WRF. In the control run, close agreement is found between the modeled wave field, and that observed by satellite. As the roughness length of the lower boundary is increased, the rate of decay is noted to increase by approximately 10% across the range of z<sub>0</sub> simulated --- although much of this increase occurs across the change from 10<\super>-2</super> m to 10<super>-1</super> m, rather than the more linear increase seen in our 2D simulations. An additional subject discussed is the generation of striations in stacked lenticular clouds. High-resolution numerical simulations show that striations in excess of 150 m in width may be generated by perturbations in the relative humidity as small as ± 0.25%. Perturbations of this scale are small enough to be likely ubiquitous in nature, explaining why these clouds always have a layered appearance.